Lahenda 3x^{2}+5x+7+2x^3+3x+16/x^2+x=10x^3+12x+4/x-2+7x^3/x+1

$$3 x ^ { 2 } + 5 x + 7 + \frac { 2 x ^ { 3 } + 3 x + 16 } { x ^ { 2 } + x } = \frac { 10 x ^ { 3 } + 12 x + 4 } { x } - \frac { 2 + 7 x ^ { 3 } } { x + 1 }$$

Lahendage ja leidke x

$$x=3$$

Juhised lineaarvõrrandi lahendamiseks

Muutuja x ei tohi võrduda ühegagi väärtustest -1,0, kuna nulliga jagamist pole määratletud. Korrutage võrrandi mõlemad pooled arvuga x\left(x+1\right), mis on arvu x^{2}+x,x,x+1 vähim ühiskordne.

$$3x^{2}x\left(x+1\right)+5xx\left(x+1\right)+x\left(x+1\right)\times 7+2x^{3}+3x+16=\left(x+1\right)\left(10x^{3}+12x+4\right)-x\left(2+7x^{3}\right)$$

Sama alusega astmete korrutamiseks liitke astendajad. Liitke 2 ja 1, et saada 3.

$$3x^{3}\left(x+1\right)+5xx\left(x+1\right)+x\left(x+1\right)\times 7+2x^{3}+3x+16=\left(x+1\right)\left(10x^{3}+12x+4\right)-x\left(2+7x^{3}\right)$$

Kasutage distributiivsusomadust, et korrutada 3x^{3} ja x+1.

$$3x^{4}+3x^{3}+5xx\left(x+1\right)+x\left(x+1\right)\times 7+2x^{3}+3x+16=\left(x+1\right)\left(10x^{3}+12x+4\right)-x\left(2+7x^{3}\right)$$

Korrutage x ja x, et leida x^{2}.

$$3x^{4}+3x^{3}+5x^{2}\left(x+1\right)+x\left(x+1\right)\times 7+2x^{3}+3x+16=\left(x+1\right)\left(10x^{3}+12x+4\right)-x\left(2+7x^{3}\right)$$

Kasutage distributiivsusomadust, et korrutada 5x^{2} ja x+1.

$$3x^{4}+3x^{3}+5x^{3}+5x^{2}+x\left(x+1\right)\times 7+2x^{3}+3x+16=\left(x+1\right)\left(10x^{3}+12x+4\right)-x\left(2+7x^{3}\right)$$

Kombineerige 3x^{3} ja 5x^{3}, et leida 8x^{3}.

$$3x^{4}+8x^{3}+5x^{2}+x\left(x+1\right)\times 7+2x^{3}+3x+16=\left(x+1\right)\left(10x^{3}+12x+4\right)-x\left(2+7x^{3}\right)$$

Kasutage distributiivsusomadust, et korrutada x ja x+1.

$$3x^{4}+8x^{3}+5x^{2}+\left(x^{2}+x\right)\times 7+2x^{3}+3x+16=\left(x+1\right)\left(10x^{3}+12x+4\right)-x\left(2+7x^{3}\right)$$

Kasutage distributiivsusomadust, et korrutada x^{2}+x ja 7.

$$3x^{4}+8x^{3}+5x^{2}+7x^{2}+7x+2x^{3}+3x+16=\left(x+1\right)\left(10x^{3}+12x+4\right)-x\left(2+7x^{3}\right)$$

Kombineerige 5x^{2} ja 7x^{2}, et leida 12x^{2}.

$$3x^{4}+8x^{3}+12x^{2}+7x+2x^{3}+3x+16=\left(x+1\right)\left(10x^{3}+12x+4\right)-x\left(2+7x^{3}\right)$$

Kombineerige 8x^{3} ja 2x^{3}, et leida 10x^{3}.

$$3x^{4}+10x^{3}+12x^{2}+7x+3x+16=\left(x+1\right)\left(10x^{3}+12x+4\right)-x\left(2+7x^{3}\right)$$

Kombineerige 7x ja 3x, et leida 10x.

$$3x^{4}+10x^{3}+12x^{2}+10x+16=\left(x+1\right)\left(10x^{3}+12x+4\right)-x\left(2+7x^{3}\right)$$

Kasutage distributiivsusomadust, et korrutada x+1 ja 10x^{3}+12x+4, ning koondage sarnased liikmed.

$$3x^{4}+10x^{3}+12x^{2}+10x+16=10x^{4}+12x^{2}+16x+10x^{3}+4-x\left(2+7x^{3}\right)$$

Kasutage distributiivsusomadust, et korrutada x ja 2+7x^{3}.

$$3x^{4}+10x^{3}+12x^{2}+10x+16=10x^{4}+12x^{2}+16x+10x^{3}+4-\left(2x+7x^{4}\right)$$

Avaldise "2x+7x^{4}" vastandi leidmiseks tuleb leida iga liikme vastand.

$$3x^{4}+10x^{3}+12x^{2}+10x+16=10x^{4}+12x^{2}+16x+10x^{3}+4-2x-7x^{4}$$

Kombineerige 16x ja -2x, et leida 14x.

$$3x^{4}+10x^{3}+12x^{2}+10x+16=10x^{4}+12x^{2}+14x+10x^{3}+4-7x^{4}$$

Kombineerige 10x^{4} ja -7x^{4}, et leida 3x^{4}.

$$3x^{4}+10x^{3}+12x^{2}+10x+16=3x^{4}+12x^{2}+14x+10x^{3}+4$$

Lahutage mõlemast poolest 3x^{4}.

$$3x^{4}+10x^{3}+12x^{2}+10x+16-3x^{4}=12x^{2}+14x+10x^{3}+4$$

Kombineerige 3x^{4} ja -3x^{4}, et leida 0.

$$10x^{3}+12x^{2}+10x+16=12x^{2}+14x+10x^{3}+4$$

Lahutage mõlemast poolest 12x^{2}.

$$10x^{3}+12x^{2}+10x+16-12x^{2}=14x+10x^{3}+4$$

Kombineerige 12x^{2} ja -12x^{2}, et leida 0.

$$10x^{3}+10x+16=14x+10x^{3}+4$$

Lahutage mõlemast poolest 14x.

$$10x^{3}+10x+16-14x=10x^{3}+4$$

Kombineerige 10x ja -14x, et leida -4x.

$$10x^{3}-4x+16=10x^{3}+4$$

Lahutage mõlemast poolest 10x^{3}.

$$10x^{3}-4x+16-10x^{3}=4$$

Kombineerige 10x^{3} ja -10x^{3}, et leida 0.

$$-4x+16=4$$

Lahutage mõlemast poolest 16.

$$-4x=4-16$$

Lahutage 16 väärtusest 4, et leida -12.

$$-4x=-12$$

Jagage mõlemad pooled -4-ga.

$$x=\frac{-12}{-4}$$

Jagage -12 väärtusega -4, et leida 3.

$$x=3$$